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arXiv · 2007.02815

Spectral heat content for α-stable processes in C1,1 open sets

Hyunchul Park·Renming Song
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Abstract

In this paper we study the asymptotic behavior, as $t\downarrow 0$, of the spectral heat content $Q^{(α)}_{D}(t)$ for isotropic $α$-stable processes, $α\in [1,2)$, in bounded $C^{1,1}$ open sets $D\subset \R^{d}$, $d\geq 2$. Together with the results from \cite{Val2017} for $d=1$ and \cite{GPS19} for $α\in (0,1)$, the main theorem of this paper establishes the asymptotic behavior of the spectral heat content up to the second term for all $α\in (0,2)$ and $d\geq1$, and resolves the conjecture raised in \cite{Val2017}.

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Hyunchul Park, Renming Song. 2023-04-21. Spectral heat content for α-stable processes in C1,1 open sets. https://arxiv.org/abs/2007.02815

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